Digital Signal Processing Reference
In-Depth Information
If
0
and
1
, the mirror boundary
are projected to an ellipse
2
220
(7)
The principal point
,
is the centre of the boundary ellipse.
The aspect ratio
⁄ ⁄
. For parameter skew
, we first compute the
eigenvectors
,
of matrix
. If the angle between eigenvectors
,
are denoted as
,
cos
. Once parameters
,
,
and
are known,
then the image plane can be transformed to a plane with
0
and
1
. In this
way, the boundary ellipse is transformed to a circle with centre
,
and a known
radius
. Once
is known, the focal length
is calculated using the formula
sin
cos1
(8)
3
VPs Detection Approach
Based on the geometric properties stated in Section 2.4 and calibration parameters
derived in Section 2.5, an approach for VPs Detection in central catadioptric image is
developed. In this section, we demonstrate how the geometric constraints are applied
in the method to reduce the search space for both CLIs and VPs detection.
3.1
Detection of CLIs from Real Images
First of all, we apply Canny edge detection to an example of catadioptric image (Fig-
ure 3(a)). The detected edge points are shown in Figure 3(b). The orientation of each
edge point is obtained after using the Canny edge detector, then the edge orientation
span is divided into a set of
k
ranges. The edges are labelled with their associated
value of
k
corresponding to the orientation range that they belong to. The edge points
from every five consecutive labels are grouped together for connected component
analysis. Edge lists formed after connected component analysis with supporting points
fewer than
pixels are removed. The results at this stage are shown in Figure 3(c).
From Figure 3(c), it is also not difficult to find out that there are mainly three types of
edge lists: first, projection of lines planar to the mirror axis, i.e. straight line segments
pointing towards the centre of the image; second, projection of parallel lines ortho-
gonal to the mirror axis; third, arc segments of mirror boundary. Following the cali-
bration process described in Section 2.5, we can fit the ellipse and carry out the circle
transformation of the image boundary to obtain image centre (Figure 3(d)). Then the
straight lines segments pointing towards the centre are grouped. A line
connecting
the endpoints
,
of each edge list is drawn and its direction
is computed.
Another line
is drawn to connect one of the endpoint
and the estimated image
centre
,
and again the line's direction
is obtained. The line segments
pointing towards the image centre can be found by using
|
|
, e.g. within
10
°
of orientation difference in our experiment. The filtered results are shown in
Figure 3(e) and (f).
